Related papers: Comparison Theorems for Stochastic Chemical Reacti…
We propose two algorithms for simulating continuous time Markov chains in the presence of metastability. We show that the algorithms correctly estimate, under the ergodicity assumption, stationary averages of the process. Both algorithms,…
Computing the stationary distributions of a continuous-time Markov chain (CTMC) involves solving a set of linear equations. In most cases of interest, the number of equations is infinite or too large, and the equations cannot be solved…
We study continuous-time Markov chains on the non-negative integers under mild regularity conditions (in particular, the set of jump vectors is finite and both forward and backward jumps are possible). Based on the so-called flux balance…
We study very simple sorting algorithms based on a probabilistic comparator model. In our model, errors in comparing two elements are due to (1) the energy or effort put in the comparison and (2) the difference between the compared…
Many dynamical systems can be successfully analyzed by representing them as networks. Empirically measured networks and dynamic processes that take place in these situations show heterogeneous, non-Markovian, and intrinsically correlated…
Counterexample generation is an indispensable part of model checking process. In stochastic model checking, counterexample generation is a challenging problem as it is not enough to find a single trace that violates the given property.…
Coupled chemical interactions in a well-mixed solution are commonly formalized as chemical reaction networks (CRNs). However, despite the widespread use of CRNs in the natural sciences, the range of computational behaviors exhibited by CRNs…
Chemical reaction networks (CRNs) are foundational models for describing complex biochemical processes. We study noncompetitive CRNs, a class of networks whose static states are rate-independent, and that can implement ReLU neural networks.…
In this work, we present a general method to establish properties of multi-dimensional continuous-time Markov chains representing stochastic reaction networks. This method consists of grouping states together (via a partition of the state…
Chemical Reaction Neural Networks (CRNNs) have emerged as an interpretable machine learning framework for discovering reaction kinetics directly from data, while strictly adhering to the Arrhenius and mass action laws. However, standard…
Molecular circuits capable of autonomous learning could unlock novel applications in fields such as bioengineering and synthetic biology. To this end, existing chemical implementations of neural computing have mainly relied on emulating…
Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are…
Highly-concurrent system models with vast state spaces like Chemical Reaction Networks (CRNs) that model biological and chemical systems pose a formidable challenge to cutting-edge formal analysis tools. Although many symbolic approaches…
While the field of first-principles explorations into chemical reaction space has been continuously growing, the development of strategies for analyzing resulting chemical reaction networks (CRNs) is lagging behind. A CRN consists of…
Steady state is an essential concept in reaction networks. Its stability reflects fundamental characteristics of several biological phenomena such as cellular signal transduction and gene expression. Because biochemical reactions occur at…
We extend the traditional framework of steady state energy transduction -- typically characterized by a single input and output -- to multi-resource transduction in open chemical reaction networks (CRNs). Transduction occurs when…
Continuous-time Markov chains (CTMCs) are popular modeling formalism that constitutes the underlying semantics for real-time probabilistic systems such as queuing networks, stochastic process algebras, and calculi for systems biology. Prism…
This work considers the method of uniformisation for continuous-time Markov chains in the context of chemical reaction networks. Previous work in the literature has shown that uniformisation can be beneficial in the context of…
Predicting stochastic cellular dynamics as emerging from the mechanistic models of molecular interactions is a long-standing challenge in systems biology: low-level chemical reaction network (CRN) models give raise to a highly-dimensional…
Inferring parameters of models of biochemical kinetics from single-cell data remains challenging because of the uncertainty arising from the intractability of the likelihood function of stochastic reaction networks. Such uncertainty falls…